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The first search for nonresonant [Formula omitted] decays is reported. The analysis uses proton-proton collision data collected with the LHCb detector between 2011 and 2018, corresponding to an integrated luminosity of 9 [Formula omitted]. No evidence for an excess of signal events over background is observed and an upper limit is set on the branching fraction ratio [Formula omitted] at [Formula omitted] confidence level. Additionally, an updated measurement of the ratio of the [Formula omitted] and [Formula omitted] branching fractions is reported. The ratio [Formula omitted] is measured to be [Formula omitted], where the first uncertainty is statistical, the second systematic, and the third is due to the uncertainties on the branching fractions of the leptonic [Formula omitted] and [Formula omitted] decays. This measurement is the most precise to date and is consistent with previous LHCb results.

The decays [Formula omitted] and [Formula omitted] are observed for the first time, in proton-proton collision data at [Formula omitted], corresponding to an integrated luminosity of 5.4 [Formula omitted] collected with the LHCb detector. Their ratios of branching fractions with respect to the [Formula omitted] mode are measured to be B[LAMBDA]b0[right arrow][LAMBDA]c+D¯0K-B[LAMBDA]b0[right arrow][LAMBDA]c+Ds-=0.1908-0.0034+0.0036-0.0018+0.0016±0.0038,B[LAMBDA]b0[right arrow][LAMBDA]c+D¯*0K-B[LAMBDA]b0[right arrow][LAMBDA]c+Ds-=0.589-0.017+0.018-0.018+0.017±0.012,B[LAMBDA]b0[right arrow][LAMBDA]c+Ds*-B[LAMBDA]b0[right arrow][LAMBDA]c+Ds-=1.668±0.022-0.055+0.061,where the first uncertainties are statistical, the second systematic, and the third, for the [Formula omitted] decays, are due to the uncertainties on the branching fractions of the [Formula omitted] and [Formula omitted] decay modes. The measured branching fractions probe factorization assumptions in effective theories and provide the normalization for future pentaquark searches in [Formula omitted] decay channels.

The [Formula omitted] and [Formula omitted] decays are observed for the first time using proton-proton collision data collected by the LHCb experiment at a centre-of-mass energy of [Formula omitted], corresponding to an integrated luminosity of [Formula omitted]. The branching fractions times the production cross-sections of [Formula omitted] baryons relative to that of [Formula omitted] baryon are measured to be R[Xi]b0[LAMBDA]b0[identical to][sigma][Xi]b0[sigma][LAMBDA]b0xB[Xi]b0[right arrow][Xi]c+Ds-B[LAMBDA]b0[right arrow][LAMBDA]c0Ds-=(15.8±1.1±0.6±7.7)%,R[Xi]b-[LAMBDA]b0[identical to][sigma][Xi]b-[sigma][LAMBDA]b0xB[Xi]b-[right arrow][Xi]c0Ds-B[LAMBDA]b0[right arrow][LAMBDA]c0Ds-=(16.9±1.3±0.9±4.3)%,where the first uncertainties are statistical, the second systematic, and the third due to the uncertainties on the decay branching fractions of relevant charmed baryons. The masses of [Formula omitted] and [Formula omitted] baryons are measured to be [Formula omitted] and [Formula omitted], where the uncertainties are statistical, systematic, and those due to charmed-hadron masses, respectively.

A model-independent study of [Formula omitted] violation in [Formula omitted] decays is presented using data corresponding to an integrated luminosity of 9 [Formula omitted] collected by the LHCb experiment at centre-of-mass energies of [Formula omitted] and 13 [Formula omitted]. The CKM angle [Formula omitted] is determined by examining the distributions of signal decays in phase-space bins of the self-conjugate [Formula omitted] decays, where [Formula omitted]. Observables related to [Formula omitted] violation are measured and the angle [Formula omitted] is determined to be [Formula omitted]. Measurements of the amplitude ratio and strong-phase difference between the favoured and suppressed [Formula omitted] decays are also presented.

Using a proton-proton collision data sample collected by the LHCb detector and corresponding to an integrated luminosity of [Formula omitted], the lifetime of the light [Formula omitted] mass eigenstate, [Formula omitted], is measured using the [Formula omitted] decay mode to be [tau]L=1.445±0.016(stat)±0.008(syst)ps.A combination of this result with a previous LHCb analysis using an independent dataset corresponding to 3 fb [Formula omitted] of integrated luminosity gives [tau]L=1.452±0.014±0.007±0.002ps,where the first uncertainty is statistical, the second due to the uncorrelated part of the systematic uncertainty and the third due to the correlated part of the systematic uncertainty.

The very rare [Formula omitted] decay is searched for by analysing [Formula omitted] decays. The analysis uses a sample of beauty mesons produced in proton-proton collisions collected with the LHCb detector between 2011 and 2018, corresponding to an integrated luminosity of 9 [Formula omitted]. The signal signature corresponds to simultaneous peaks in the [Formula omitted] and [Formula omitted] invariant masses. No evidence for an excess of events over background is observed and an upper limit is set on the branching fraction of the decay at [Formula omitted] at [Formula omitted] confidence level. This is the first limit on the branching fraction of [Formula omitted] decays and the most stringent limit on [Formula omitted] decays to leptonic final states. The analysis is the first search for a rare charm-meson decay exploiting production via beauty decays.

The first measurement of [Formula omitted] and [Formula omitted] production in PbNe collisions by the LHCb experiment in its fixed-target configuration is reported. The production of [Formula omitted] and [Formula omitted] mesons is studied with a beam of lead ions with an energy of 2.5 [Formula omitted] per nucleon colliding on gaseous neon targets at rest, corresponding to a nucleon-nucleon centre-of-mass energy of [Formula omitted]. The [Formula omitted]/ [Formula omitted] production cross-section ratio is studied as a function of rapidity, transverse momentum and collision centrality. These data are compared with measurements from [Formula omitted] collisions at the same energy and show no difference in the observed [Formula omitted] suppression trend when comparing [Formula omitted] and PbNe peripheral collisions with PbNe central collisions.

The measurement of charmonium states produced in proton-neon ( [Formula omitted]) collisions by the LHCb experiment in its fixed-target configuration is presented. The production of [Formula omitted] and [Formula omitted] mesons is studied with a beam of 2.5 [Formula omitted] protons colliding on gaseous neon targets at rest, corresponding to a nucleon-nucleon centre-of-mass energy [Formula omitted]. The data sample corresponds to an integrated luminosity of [Formula omitted] nb [Formula omitted]. The [Formula omitted] and [Formula omitted] hadrons are reconstructed in [Formula omitted] [Formula omitted] final states. The [Formula omitted] production cross-section per target nucleon in the centre-of-mass rapidity range [Formula omitted] is found to be [Formula omitted]. The ratio of [Formula omitted] and [Formula omitted] cross-sections is evaluated to [Formula omitted]. The [Formula omitted] to [Formula omitted] relative production rate is found to be [Formula omitted] in good agreement with other measurements involving beam and target nuclei of similar sizes.